# Optional break homework/skills practice

Hey guys – The following exercises are optional and are intended as a way for you to maintain your skills and review over the break. Work through them if you want and if there are any that you have trouble with come to Learning Commons.

1. Simplify $\sqrt[3]{(x^3 y)^2 y^4}$

2. Simplify $\frac{x^4(3x)^2}{x^3}$

3. Solve for x $\frac{x}{x+2}-3=\frac{1}{x+2}$

4. Solve for x $\frac{1}{x}+\frac{2}{x-1}=3$

5. Graph $y=\frac{x^2-4}{x^3+8}$

6. Graph $y=\frac{x^3}{x^2-1}$

7. Graph $y=-2^{-x}-2$

8. Graph $y=10^{x-2}+1$

9. Solve for x $2^x-1=7$

10. When a certain medical drug is administered to a patient, the number of milligrams remaining in the patient’s bloodstream after t hours is modeled by $D(t)=50e^{-0.2t}$. How many milligrams of the drug remain in the patient’s bloodstream after 3 hours?